1. Field of the Invention
The invention relates to a method of forming fine patterns, employing a mask for projection and an electron beam, and a method for fabricating a semiconductor device, using the same.
2. Description of the Related Art
With a method of forming patterns, employing an electron beam, the electron beam with which a substrate with a resist film formed on the surface thereof is irradiated scatters inside the substrate, and returns towards the resist film on which the patterns are to be fabricated across a wide range of the resist film, thereby causing a phenomenon wherein the deposition energy of the electron beam is nonuniformly distributed depending on dimensions and disposition of patterns in the vicinity thereof. As a result, deviation from design dimensions occurs to dimensions of a finished resist. This is called a proximity effect. A range affected by the proximity effect varies depending on an acceleration voltage of an electron beam, and electrons emitted at an acceleration voltage of, for example, 100 kV affect across a range within the substrate, not less than 30 μm in radius from a point of radiation, causing a change in the dimensions of patterns. Accordingly, there is the need for properly correcting the proximity effect in order to implement exposure with high precision
Further, there has been a problem of low throughput with electron beam lithography because it is a method whereby small patterns are exposed in sequence, however, advance has been made recently in commercial application of a method with a throughput largely improved by use of a large area mask for projection. This method is generally called electron projection lithography (referred to hereinafter as EPL). With the EPL, a range subjected to exposure at one time is called a sub-field, and the sub-field has an area about 250 μm square. In the case of the above-described example, the range affected by the proximity effect is a range in the order of not less than 30 μm in radius, so that the proximity effect within the sub-field nonuniformly appears depending on the disposition of patterns. Consequently, it is not possible to employ a method for obtaining optimum dimensions of the patterns by varying intensity of exposure for every pattern to be exposed, which has been commonly practiced in the case of the conventional electron beam direct lithography without use of a mask for projection.
One method for correcting the proximity effect with EPL method is an auxiliary exposure method. This method is a method whereby nonuniformity in distribution of the deposition energy of an electron beam due to backscattering thereof, caused by nonuniformity of exposure patterns, is rendered uniform by virtue of auxiliary exposure. Since the effect of the backscattering is decreased in a sparse pattern region of the exposure patterns, auxiliary exposure is applied to the sparse pattern region. More specifically, this is attained by exposing patterns with tone reversed from that of the exposure patterns with an adequate intensity of exposure such that an extent of an electron beam blur is approximate to a range of backscattering. The largest advantage of the method is that complex calculation for the proximity effect is not required. However, since it becomes necessary to execute the auxiliary exposure in addition to exposure with exposure patterns, originally intended for, there have arisen problems with this method in that a mask for the auxiliary exposure is required, and throughput is in effect decreased due to exposure to be executed twice. Furthermore, because the auxiliary exposure results in subjecting regions other than regions of the exposure patterns to exposure, there has arisen another problem as well of inviting a drop in contrast of the deposition energy between patterned parts and unpatterned parts.
As a different EPL method of correcting the proximity effect, there is available a method of pattern modification. This is a method for causing mask patterns to be modified beforehand in anticipation of the patterns undergoing deformation after exposure due to the proximity effect. With this method, dimensions of mask pattern modification are set such that the finished dimensions of the mask patterns correspond to a design dimensions as a result of original dimensions thereof undergoing a change after exposure due to the proximity effect. The method is advantageous in that once an adequate mask is formed, exposure can be executed without taking into consideration the proximity effect at the time exposure. Further, since there is no need for executing exposure twice, there occurs no problem of a decrease in throughput. On the other hand, there has been a drawback with the method in that calculation of the dimensions of the mask pattern modification involves complex operation, requiring processing with a computer for many hours. Accordingly, as disclosed in, for example, Journal of Vacuum Science and Technology, Vol. B9 pp. 3048-3053, No. 6, November/December, 1991, there has been adopted a correction method based on the so-called rule-base wherein patterns having the same characteristic are grouped together to thereby decide upon modifying pattern dimension. Further, there has been disclosed a method for correction of the proximity effect through correction of intensity of exposure by use of a pattern area density map in JP-A No. 225816/1991. Similarly, a method of deciding upon dimensions of pattern modification by use of a pattern area density map in Japanese Journal of Applied Physics Vol. 37, pp. 6767-6773, No. 12B, December, 1998.
However, the conventional methods as described above have the following drawbacks. Firstly, with the method of subjecting a large area en bloc to exposure, a multitude of electrons reside in an electronic optical system, thereby causing a problem of a change occurring to an extent of electron beam blur by the agency of space charge. This is generally called a Coulomb effect. Total electric current varies on the basis of a unit of the previously described sub-field by each of the exposure patterns, so that the extent of the electron beam blur varies by a unit of the sub-field due to the Coulomb effect. Furthermore, the Coulomb effect is not necessarily constant even within the sub-field, so that the electron beam blur undergoes local changes depending on pattern sparseness or pattern denseness (this is referred to herein as local Coulomb effect). With the conventional methods, there has not been executed any correction for the proximity effect, taking into consideration as much as the local Coulomb effect.
Secondly, for effecting correction for the proximity effect, there is the need for establishing dimensions of pattern modification by taking into consideration the extent of the electron beam blur, dependent on aberration of an optical system and the Coulomb effect, and backscattering, however, since modification of the patterns causes other patterns to be affected, it is therefore necessary to establish dimensions of pattern modification, mutually uncontradictory to all the patterns, generally as the solution of simultaneous equations. This has raised a problem in that a great deal of time is required for calculation in the case of a complex LSI pattern of today.
Further, instead of finding the solution of the simultaneous equations, there are conceivable means for causing mutual effects on the patterns, accompanying modification of the patterns, to be converged by repeated computation. In such a case, the dimensions of pattern modification are expressed by the function of the pattern area density and the extent of the electron beam blur, and can therefore be found by solving linear equations. However, since it is necessary to repeat modification of the patterns and calculation of pattern areas for establishing the dimensions of pattern modification as the solution of the linear equations, it is still unavoidable to take a great deal of time for calculation.
Thirdly, with computation for complementary division, sub-field division, and correction for the proximity effect, there is the need for executing complex pattern computations with respect to massive LSI data. Normally, layout data of an LSI are processed as hierarchical data, thereby compressing an amount of the data to one several tenths thereof or less. With the conventional method, however, those processing are executed with respect to flat-structure data for every sub-field, so that it is not possible to make use of advantageous effects of the hierarchical data, thus causing a major problem in terms of process time and data handling.